Related papers: Fair Measures for Countable-to-one Maps
Graphs are used in almost every scientific discipline to express relations among a set of objects. Algorithms that compare graphs, and output a closeness score, or a correspondence among their nodes, are thus extremely important. Despite…
Locational measures of accessibility are widely used in urban and transportation planning to understand the impact of the transportation system on influencing people's access to places. However, there is a considerable lack of measurement…
Algorithmic decisions about individuals require predictions that are not only accurate but also fair with respect to sensitive attributes such as gender and race. Causal notions of fairness align with legal requirements, yet many methods…
In this note, continuous transitive maps $f$ on the interval $I$ are re-addressed, where $I$ denotes one of the intervals: $(-\infty, \infty)$, $(-\infty, a]$, $[b, \infty)$, $[a, b]$, where $a < b$ are real numbers. Such maps must have a…
Using the technique of the metrization theorem of uniformities with countable bases, in this note we provide, test and compare an explicit algorithm to produce a metric $d(x,y)$ between the vertices $x$ and $y$ of an affinity weighted…
Algorithmic and statistical approaches to congressional redistricting are becoming increasingly valuable tools in courts and redistricting commissions for quantifying gerrymandering in the United States. While there is existing literature…
Machine Learning algorithms are ubiquitous in key decision-making contexts such as justice, healthcare and finance, which has spawned a great demand for fairness in these procedures. However, the theoretical properties of such models in…
In this paper, we defined three kinds of measures depending on the given finite directed graphs. For the given finite directed graph, we can construct the free semigroupoid, the diagram set and the reduced diagram set, as algebraic…
In this paper, we study the problem of fair classification in the presence of prior probability shifts, where the training set distribution differs from the test set. This phenomenon can be observed in the yearly records of several…
The study of very large graphs is a prominent theme in modern-day mathematics. In this paper we develop a rigorous foundation for studying the space of finite labelled graphs and their limits. These limiting objects are naturally countable…
We study the statistical properties of piecewise expanding maps in the general setting of metric measure spaces. We provide sufficient conditions for exponential mixing of such systems with explicit estimates on the constants. We also…
Countable state Markov shifts are a natural generalization of the well-known subshifts of finite type. They are the subject of current research both for their own sake and as models for smooth dynamical systems. In this paper, we…
It is of critical importance to be aware of the historical discrimination embedded in the data and to consider a fairness measure to reduce bias throughout the predictive modeling pipeline. Given various notions of fairness defined in the…
We provide a quantification of the uniqueness of Gibbs measure for topologically mixing countable Markov shifts with locally H\"older continuous potentials. Corollaries for speed of convergence for approximation by finite subsystems are…
The seminal work of Dwork {\em et al.} [ITCS 2012] introduced a metric-based notion of individual fairness. Given a task-specific similarity metric, their notion required that every pair of similar individuals should be treated similarly.…
Nowadays, the analysis of complex phenomena modeled by graphs plays a crucial role in many real-world application domains where decisions can have a strong societal impact. However, numerous studies and papers have recently revealed that…
A marked metric measure space (mmm-space) is a triple (X,r,mu), where (X,r) is a complete and separable metric space and mu is a probability measure on XxI for some Polish space I of possible marks. We study the space of all (equivalence…
In 2007 H. Long-Guang and Z. Xian, [H. Long-Guang and Z. Xian, Cone Metric Spaces and Fixed Point Theorems of Contractive Mapping, J. Math. Anal. Appl., 322(2007), 1468-1476], generalized the concept of a metric space, by introducing cone…
A clustering may be considered as fair on pre-specified sensitive attributes if the proportions of sensitive attribute groups in each cluster reflect that in the dataset. In this paper, we consider the task of fair clustering for scenarios…
In recent years, in an effort to promote fairness in the election process, a wide variety of techniques and metrics have been proposed to determine whether a map is a partisan gerrymander. The most accessible measures, requiring easily…